How did the British end salutary neglect?

Salutary neglect was an approach to policy that successive British governments adopted towards the American colonies up until the late 18th century. Essentially, it meant the government in London wouldn't try to enforce existing trade laws and regulations too harshly. Instead, they would allow the American colonists a fair amount of leeway in how they interpreted the relevant laws.

Such a lenient approach was thought essential to maintaining good order in the colonies. It was widely held that if the government were too strict in its enforcement of trade laws then this would unduly antagonize the American colonists, potentially damaging the economic life of the colonies as well as leading to outbreaks of civil disorder.

The prevailing attitude changed in the wake of Great Britain's victory in the Seven Years' War. Now that the British were in charge of vast swathes of new territory which they'd taken from the French, it was felt necessary to exert greater control over the political and economic life of the American colonies. This largely took the form of tighter regulations on trade, such as the Stamp Act and Quebec Act, which caused widespread resentment right throughout the colonies.

The main problem was that, due largely to the policy of salutary neglect, the American colonists had grown accustomed to controlling their own affairs. So when the British started passing new trade legislation, and enforcing it rigorously, Americans became enraged at what they saw as a flagrant attack upon their liberties. It's not an exaggeration to say that the end of salutary neglect marked the beginning of the end for British rule in America.

Why did the British allow salutary neglect?

Salutary neglect was, in many respects, shaped by practical realities, given the technological limitations of the time. With an entire ocean separating England and the colonies, in a time period lacking modern communications and transportation, the sheer distance involved was too great to justify a particularly interventionist colonial policy. In many respects, the rewards wouldn't have been worth the costs. That being said, you'll find this calculus will start to change following the French and Indian War.

For an additional layer of context, I would add that colonization (as well as most expeditions which would have been global in scope) was inherently a high-risk proposition, and the English government tended to have a history of divesting itself of a significant amount of this burden. For example, if you were to look at the thirteen original colonies, what you'll find is that every one of them started out as either a proprietary or joint-stock company colony.